/* Copyright 2002-2024 CS GROUP
    * Licensed to CS GROUP (CS) under one or more
    * contributor license agreements.  See the NOTICE file distributed with
    * this work for additional information regarding copyright ownership.
    * CS licenses this file to You under the Apache License, Version 2.0
    * (the "License"); you may not use this file except in compliance with
    * the License.  You may obtain a copy of the License at
    *
    *   http://www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License.
   */
  package org.orekit.time;
  
  import java.io.Serializable;
  import java.time.Instant;
  import java.time.LocalDateTime;
  import java.time.ZoneOffset;
  import java.time.format.DateTimeFormatter;
  import java.util.Date;
  import java.util.TimeZone;
  
  import java.util.concurrent.TimeUnit;
  import org.hipparchus.util.FastMath;
  import org.orekit.annotation.DefaultDataContext;
  import org.orekit.data.DataContext;
  import org.orekit.errors.OrekitIllegalArgumentException;
  import org.orekit.utils.Constants;
  
  /** This class represents a specific instant in time.
  
   * <p>Instances of this class are considered to be absolute in the sense
   * that each one represent the occurrence of some event and can be compared
   * to other instances or located in <em>any</em> {@link TimeScale time scale}. In
   * other words the different locations of an event with respect to two different
   * time scales (say {@link TAIScale TAI} and {@link UTCScale UTC} for example) are
   * simply different perspective related to a single object. Only one
   * <code>AbsoluteDate</code> instance is needed, both representations being available
   * from this single instance by specifying the time scales as parameter when calling
   * the ad-hoc methods.</p>
   *
   * <p>Since an instance is not bound to a specific time-scale, all methods related
   * to the location of the date within some time scale require to provide the time
   * scale as an argument. It is therefore possible to define a date in one time scale
   * and to use it in another one. An example of such use is to read a date from a file
   * in UTC and write it in another file in TAI. This can be done as follows:</p>
   * <pre>
   *   DateTimeComponents utcComponents = readNextDate();
   *   AbsoluteDate date = new AbsoluteDate(utcComponents, TimeScalesFactory.getUTC());
   *   writeNextDate(date.getComponents(TimeScalesFactory.getTAI()));
   * </pre>
   *
   * <p>Two complementary views are available:</p>
   * <ul>
   *   <li><p>location view (mainly for input/output or conversions)</p>
   *   <p>locations represent the coordinate of one event with respect to a
   *   {@link TimeScale time scale}. The related methods are {@link
   *   #AbsoluteDate(DateComponents, TimeComponents, TimeScale)}, {@link
   *   #AbsoluteDate(int, int, int, int, int, double, TimeScale)}, {@link
   *   #AbsoluteDate(int, int, int, TimeScale)}, {@link #AbsoluteDate(Date,
   *   TimeScale)}, {@link #parseCCSDSCalendarSegmentedTimeCode(byte, byte[])},
   *   {@link #toDate(TimeScale)}, {@link #toString(TimeScale) toString(timeScale)},
   *   {@link #toString()}, and {@link #timeScalesOffset}.</p>
   *   </li>
   *   <li><p>offset view (mainly for physical computation)</p>
   *   <p>offsets represent either the flow of time between two events
   *   (two instances of the class) or durations. They are counted in seconds,
   *   are continuous and could be measured using only a virtually perfect stopwatch.
   *   The related methods are {@link #AbsoluteDate(AbsoluteDate, double)},
   *   {@link #parseCCSDSUnsegmentedTimeCode(byte, byte, byte[], AbsoluteDate)},
   *   {@link #parseCCSDSDaySegmentedTimeCode(byte, byte[], DateComponents)},
   *   {@link #durationFrom(AbsoluteDate)}, {@link #compareTo(TimeOffset)}, {@link #equals(Object)}
   *   and {@link #hashCode()}.</p>
   *   </li>
   * </ul>
   * <p>
   * A few reference epochs which are commonly used in space systems have been defined. These
   * epochs can be used as the basis for offset computation. The supported epochs are:
   * {@link #JULIAN_EPOCH}, {@link #MODIFIED_JULIAN_EPOCH}, {@link #FIFTIES_EPOCH},
   * {@link #CCSDS_EPOCH}, {@link #GALILEO_EPOCH}, {@link #GPS_EPOCH}, {@link #QZSS_EPOCH}
   * {@link #J2000_EPOCH}, {@link #JAVA_EPOCH}.
   * There are also two factory methods {@link #createJulianEpoch(double)}
   * and {@link #createBesselianEpoch(double)} that can be used to compute other reference
   * epochs like J1900.0 or B1950.0.
   * In addition to these reference epochs, two other constants are defined for convenience:
   * {@link #PAST_INFINITY} and {@link #FUTURE_INFINITY}, which can be used either as dummy
   * dates when a date is not yet initialized, or for initialization of loops searching for
   * a min or max date.
   * </p>
   * <p>
   * Instances of the <code>AbsoluteDate</code> class are guaranteed to be immutable.
   * </p>
   * @author Luc Maisonobe
   * @author Evan Ward
   * @see TimeScale
  * @see TimeStamped
  * @see ChronologicalComparator
  */
 public class AbsoluteDate
     extends TimeOffset
     implements TimeStamped, TimeShiftable<AbsoluteDate>, Comparable<TimeOffset>, Serializable {
 
     /** Reference epoch for julian dates: -4712-01-01T12:00:00 Terrestrial Time.
      * <p>Both <code>java.util.Date</code> and {@link DateComponents} classes
      * follow the astronomical conventions and consider a year 0 between
      * years -1 and +1, hence this reference date lies in year -4712 and not
      * in year -4713 as can be seen in other documents or programs that obey
      * a different convention (for example the <code>convcal</code> utility).</p>
      *
      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
      *
      * @see TimeScales#getJulianEpoch()
      */
     @DefaultDataContext
     public static final AbsoluteDate JULIAN_EPOCH = DataContext.getDefault().getTimeScales().getJulianEpoch();
 
     /** Reference epoch for modified julian dates: 1858-11-17T00:00:00 Terrestrial Time.
      *
      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
      *
      * @see TimeScales#getModifiedJulianEpoch()
      */
     @DefaultDataContext
     public static final AbsoluteDate MODIFIED_JULIAN_EPOCH = DataContext.getDefault().getTimeScales().getModifiedJulianEpoch();
 
     /** Reference epoch for 1950 dates: 1950-01-01T00:00:00 Terrestrial Time.
      *
      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
      *
      * @see TimeScales#getFiftiesEpoch()
      */
     @DefaultDataContext
     public static final AbsoluteDate FIFTIES_EPOCH = DataContext.getDefault().getTimeScales().getFiftiesEpoch();
 
     /** Reference epoch for CCSDS Time Code Format (CCSDS 301.0-B-4):
      * 1958-01-01T00:00:00 International Atomic Time (<em>not</em> UTC).
      *
      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
      *
      * @see TimeScales#getCcsdsEpoch()
      */
     @DefaultDataContext
     public static final AbsoluteDate CCSDS_EPOCH = DataContext.getDefault().getTimeScales().getCcsdsEpoch();
 
     /** Reference epoch for Galileo System Time: 1999-08-22T00:00:00 GST.
      *
      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
      *
      * @see TimeScales#getGalileoEpoch()
      */
     @DefaultDataContext
     public static final AbsoluteDate GALILEO_EPOCH = DataContext.getDefault().getTimeScales().getGalileoEpoch();
 
     /** Reference epoch for GPS weeks: 1980-01-06T00:00:00 GPS time.
      *
      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
      *
      * @see TimeScales#getGpsEpoch()
      */
     @DefaultDataContext
     public static final AbsoluteDate GPS_EPOCH = DataContext.getDefault().getTimeScales().getGpsEpoch();
 
     /** Reference epoch for QZSS weeks: 1980-01-06T00:00:00 QZSS time.
      *
      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
      *
      * @see TimeScales#getQzssEpoch()
      */
     @DefaultDataContext
     public static final AbsoluteDate QZSS_EPOCH = DataContext.getDefault().getTimeScales().getQzssEpoch();
 
     /** Reference epoch for IRNSS weeks: 1999-08-22T00:00:00 IRNSS time.
      *
      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
      *
      * @see TimeScales#getIrnssEpoch()
      */
     @DefaultDataContext
     public static final AbsoluteDate IRNSS_EPOCH = DataContext.getDefault().getTimeScales().getIrnssEpoch();
 
     /** Reference epoch for BeiDou weeks: 2006-01-01T00:00:00 UTC.
      *
      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
      *
      * @see TimeScales#getBeidouEpoch()
      */
     @DefaultDataContext
     public static final AbsoluteDate BEIDOU_EPOCH = DataContext.getDefault().getTimeScales().getBeidouEpoch();
 
     /** Reference epoch for GLONASS four-year interval number: 1996-01-01T00:00:00 GLONASS time.
      * <p>By convention, TGLONASS = UTC + 3 hours.</p>
      *
      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
      *
      * @see TimeScales#getGlonassEpoch()
      */
     @DefaultDataContext
     public static final AbsoluteDate GLONASS_EPOCH = DataContext.getDefault().getTimeScales().getGlonassEpoch();
 
     /** J2000.0 Reference epoch: 2000-01-01T12:00:00 Terrestrial Time (<em>not</em> UTC).
      *
      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
      *
      * @see #createJulianEpoch(double)
      * @see #createBesselianEpoch(double)
      * @see TimeScales#getJ2000Epoch()
      */
     @DefaultDataContext
     public static final AbsoluteDate J2000_EPOCH = DataContext.getDefault().getTimeScales().getJ2000Epoch();
 
     /** Java Reference epoch: 1970-01-01T00:00:00 Universal Time Coordinate.
      * <p>
      * Between 1968-02-01 and 1972-01-01, UTC-TAI = 4.213 170 0s + (MJD - 39 126) x 0.002 592s.
      * As on 1970-01-01 MJD = 40587, UTC-TAI = 8.000082s
      * </p>
      *
      * <p>This constant uses the {@link DataContext#getDefault() default data context}.
      *
      * @see TimeScales#getJavaEpoch()
      */
     @DefaultDataContext
     public static final AbsoluteDate JAVA_EPOCH = DataContext.getDefault().getTimeScales().getJavaEpoch();
 
     /**
      * An arbitrary finite date. Uses when a non-null date is needed but its value doesn't
      * matter.
      */
     public static final AbsoluteDate ARBITRARY_EPOCH = new AbsoluteDate(TimeOffset.ZERO);
 
     /** Dummy date at infinity in the past direction.
      * @see TimeScales#getPastInfinity()
      */
     public static final AbsoluteDate PAST_INFINITY = ARBITRARY_EPOCH.shiftedBy(Double.NEGATIVE_INFINITY);
 
     /** Dummy date at infinity in the future direction.
      * @see TimeScales#getFutureInfinity()
      */
     public static final AbsoluteDate FUTURE_INFINITY = ARBITRARY_EPOCH.shiftedBy(Double.POSITIVE_INFINITY);
 
     /** Serializable UID. */
     private static final long serialVersionUID = 20240711L;
 
     /** Create an instance with a default value ({@link #J2000_EPOCH}).
      *
      * <p>This constructor uses the {@link DataContext#getDefault() default data context}.
      *
      * @see #AbsoluteDate(DateTimeComponents, TimeScale)
      */
     @DefaultDataContext
     public AbsoluteDate() {
         super(J2000_EPOCH.getSeconds(), J2000_EPOCH.getAttoSeconds());
     }
 
     /** Build an instance from a location (parsed from a string) in a {@link TimeScale time scale}.
      * <p>
      * The supported formats for location are mainly the ones defined in ISO-8601 standard,
      * the exact subset is explained in {@link DateTimeComponents#parseDateTime(String)},
      * {@link DateComponents#parseDate(String)} and {@link TimeComponents#parseTime(String)}.
      * </p>
      * <p>
      * As CCSDS ASCII calendar segmented time code is a trimmed down version of ISO-8601,
      * it is also supported by this constructor.
      * </p>
      * @param location location in the time scale, must be in a supported format
      * @param timeScale time scale
      * @exception IllegalArgumentException if location string is not in a supported format
      */
     public AbsoluteDate(final String location, final TimeScale timeScale) {
         this(DateTimeComponents.parseDateTime(location), timeScale);
     }
 
     /** Build an instance from a location in a {@link TimeScale time scale}.
      * @param location location in the time scale
      * @param timeScale time scale
      */
     public AbsoluteDate(final DateTimeComponents location, final TimeScale timeScale) {
         this(location.getDate(), location.getTime(), timeScale);
     }
 
     /** Build an instance from a location in a {@link TimeScale time scale}.
      * @param date date location in the time scale
      * @param time time location in the time scale
      * @param timeScale time scale
      */
     public AbsoluteDate(final DateComponents date, final TimeComponents time,
                         final TimeScale timeScale) {
         // epoch is at 12:00 (close to J2000.0, but in TAI scale), hence the subtraction of 720 minutes
         super(new TimeOffset(60L * ((date.getJ2000Day() * 24L + time.getHour()) * 60L +
                               time.getMinute() - time.getMinutesFromUTC() - 720L),
                              0L),
               time.getSplitSecond(),
               timeScale.offsetToTAI(date, time));
     }
 
     /** Build an instance from a location in a {@link TimeScale time scale}.
      * @param year year number (may be 0 or negative for BC years)
      * @param month month number from 1 to 12
      * @param day day number from 1 to 31
      * @param hour hour number from 0 to 23
      * @param minute minute number from 0 to 59
      * @param second second number from 0.0 to 60.0 (excluded)
      * @param timeScale time scale
      * @exception IllegalArgumentException if inconsistent arguments
      * are given (parameters out of range)
      */
     public AbsoluteDate(final int year, final int month, final int day,
                         final int hour, final int minute, final double second,
                         final TimeScale timeScale) throws IllegalArgumentException {
         this(year, month, day, hour, minute, new TimeOffset(second), timeScale);
     }
 
     /** Build an instance from a location in a {@link TimeScale time scale}.
      * @param year year number (may be 0 or negative for BC years)
      * @param month month number from 1 to 12
      * @param day day number from 1 to 31
      * @param hour hour number from 0 to 23
      * @param minute minute number from 0 to 59
      * @param second second number from 0.0 to 60.0 (excluded)
      * @param timeScale time scale
      * @exception IllegalArgumentException if inconsistent arguments
      * are given (parameters out of range)
      * @since 13.0
      */
     public AbsoluteDate(final int year, final int month, final int day,
                         final int hour, final int minute, final TimeOffset second,
                         final TimeScale timeScale) throws IllegalArgumentException {
         this(new DateComponents(year, month, day), new TimeComponents(hour, minute, second), timeScale);
     }
 
     /** Build an instance from a location in a {@link TimeScale time scale}.
      * @param year year number (may be 0 or negative for BC years)
      * @param month month enumerate
      * @param day day number from 1 to 31
      * @param hour hour number from 0 to 23
      * @param minute minute number from 0 to 59
      * @param second second number from 0.0 to 60.0 (excluded)
      * @param timeScale time scale
      * @exception IllegalArgumentException if inconsistent arguments
      * are given (parameters out of range)
      */
     public AbsoluteDate(final int year, final Month month, final int day,
                         final int hour, final int minute, final double second,
                         final TimeScale timeScale) throws IllegalArgumentException {
         this(year, month, day, hour, minute, new TimeOffset(second), timeScale);
     }
 
     /** Build an instance from a location in a {@link TimeScale time scale}.
      * @param year year number (may be 0 or negative for BC years)
      * @param month month enumerate
      * @param day day number from 1 to 31
      * @param hour hour number from 0 to 23
      * @param minute minute number from 0 to 59
      * @param second second number from 0.0 to 60.0 (excluded)
      * @param timeScale time scale
      * @exception IllegalArgumentException if inconsistent arguments
      * are given (parameters out of range)
      * @since 13.0
      */
     public AbsoluteDate(final int year, final Month month, final int day,
                         final int hour, final int minute, final TimeOffset second,
                         final TimeScale timeScale) throws IllegalArgumentException {
         this(new DateComponents(year, month, day), new TimeComponents(hour, minute, second), timeScale);
     }
 
     /** Build an instance from a location in a {@link TimeScale time scale}.
      * <p>The hour is set to 00:00:00.000.</p>
      * @param date date location in the time scale
      * @param timeScale time scale
      * @exception IllegalArgumentException if inconsistent arguments
      * are given (parameters out of range)
      */
     public AbsoluteDate(final DateComponents date, final TimeScale timeScale)
         throws IllegalArgumentException {
         this(date, TimeComponents.H00, timeScale);
     }
 
     /** Build an instance from a location in a {@link TimeScale time scale}.
      * <p>The hour is set to 00:00:00.000.</p>
      * @param year year number (may be 0 or negative for BC years)
      * @param month month number from 1 to 12
      * @param day day number from 1 to 31
      * @param timeScale time scale
      * @exception IllegalArgumentException if inconsistent arguments
      * are given (parameters out of range)
      */
     public AbsoluteDate(final int year, final int month, final int day,
                         final TimeScale timeScale) throws IllegalArgumentException {
         this(new DateComponents(year, month, day), TimeComponents.H00, timeScale);
     }
 
     /** Build an instance from a location in a {@link TimeScale time scale}.
      * <p>The hour is set to 00:00:00.000.</p>
      * @param year year number (may be 0 or negative for BC years)
      * @param month month enumerate
      * @param day day number from 1 to 31
      * @param timeScale time scale
      * @exception IllegalArgumentException if inconsistent arguments
      * are given (parameters out of range)
      */
     public AbsoluteDate(final int year, final Month month, final int day,
                         final TimeScale timeScale) throws IllegalArgumentException {
         this(new DateComponents(year, month, day), TimeComponents.H00, timeScale);
     }
 
     /** Build an instance from a location in a {@link TimeScale time scale}.
      * @param location location in the time scale
      * @param timeScale time scale
      */
     public AbsoluteDate(final Date location, final TimeScale timeScale) {
         this(new DateComponents(DateComponents.JAVA_EPOCH, (int) (location.getTime() / 86400000L)),
              new TimeComponents(new TimeOffset(location.getTime() % 86400000L, TimeOffset.MILLISECOND)),
              timeScale);
     }
 
     /** Build an instance from an {@link Instant instant} in utc time scale.
      * @param instant instant in the time scale
      * @since 12.1
      */
     @DefaultDataContext
     public AbsoluteDate(final Instant instant) {
         this(instant, TimeScalesFactory.getUTC());
     }
 
     /** Build an instance from an {@link Instant instant} in the {@link UTCScale time scale}.
      * @param instant instant in the time scale
      * @param utcScale utc time scale
      * @since 12.1
      */
     public AbsoluteDate(final Instant instant, final UTCScale utcScale) {
         this(new DateComponents(DateComponents.JAVA_EPOCH, (int) (instant.getEpochSecond() / 86400L)),
              new TimeComponents(TimeOffset.SECOND.multiply(instant.getEpochSecond() % 86400L).
                                 add(new TimeOffset(instant.getNano(), TimeUnit.NANOSECONDS))),
              utcScale);
     }
 
     /** Build an instance from an elapsed duration since another instant.
      * <p>It is important to note that the elapsed duration is <em>not</em>
      * the difference between two readings on a time scale. As an example,
      * the duration between the two instants leading to the readings
      * 2005-12-31T23:59:59 and 2006-01-01T00:00:00 in the {@link UTCScale UTC}
      * time scale is <em>not</em> 1 second, but a stop watch would have measured
      * an elapsed duration of 2 seconds between these two instances because a leap
      * second was introduced at the end of 2005 in this time scale.</p>
      * <p>This constructor is the reverse of the {@link #durationFrom(AbsoluteDate)}
      * method.</p>
      * @param since start instant of the measured duration
      * @param elapsedDuration physically elapsed duration from the <code>since</code>
      * instant, as measured in a regular time scale
      * @see #durationFrom(AbsoluteDate)
      */
     public AbsoluteDate(final AbsoluteDate since, final double elapsedDuration) {
         this(since, new TimeOffset(elapsedDuration));
     }
 
     /** Build an instance from an elapsed duration since another instant.
      * <p>It is important to note that the elapsed duration is <em>not</em>
      * the difference between two readings on a time scale. As an example,
      * the duration between the two instants leading to the readings
      * 2005-12-31T23:59:59 and 2006-01-01T00:00:00 in the {@link UTCScale UTC}
      * time scale is <em>not</em> 1 second, but a stop watch would have measured
      * an elapsed duration of 2 seconds between these two instances because a leap
      * second was introduced at the end of 2005 in this time scale.</p>
      * <p>This constructor is the reverse of the {@link #durationFrom(AbsoluteDate)}
      * method.</p>
      * @param since start instant of the measured duration
      * @param elapsedDuration physically elapsed duration from the <code>since</code>
      * instant, as measured in a regular time scale
      * @see #durationFrom(AbsoluteDate)
      * @since 13.0
      */
     public AbsoluteDate(final AbsoluteDate since, final TimeOffset elapsedDuration) {
         super(since, elapsedDuration);
     }
 
     /** Build an instance from an elapsed duration since another instant.
      * <p>It is important to note that the elapsed duration is <em>not</em>
      * the difference between two readings on a time scale. As an example,
      * the duration between the two instants leading to the readings
      * 2005-12-31T23:59:59 and 2006-01-01T00:00:00 in the {@link UTCScale UTC}
      * time scale is <em>not</em> 1 second, but a stop watch would have measured
      * an elapsed duration of 2 seconds between these two instances because a leap
      * second was introduced at the end of 2005 in this time scale.</p>
      * <p>This constructor is the reverse of the {@link #durationFrom(AbsoluteDate, TimeUnit)}
      * method.</p>
      * @param since start instant of the measured duration
      * @param elapsedDuration physically elapsed duration from the <code>since</code>
      * instant, as measured in a regular time scale
      * @param timeUnit {@link TimeUnit} of the elapsedDuration
      * @see #durationFrom(AbsoluteDate, TimeUnit)
      * @since 12.1
      */
     public AbsoluteDate(final AbsoluteDate since, final long elapsedDuration, final TimeUnit timeUnit) {
         this(since, new TimeOffset(elapsedDuration, timeUnit));
     }
 
     /** Build an instance from an apparent clock offset with respect to another
      * instant <em>in the perspective of a specific {@link TimeScale time scale}</em>.
      * <p>It is important to note that the apparent clock offset <em>is</em> the
      * difference between two readings on a time scale and <em>not</em> an elapsed
      * duration. As an example, the apparent clock offset between the two instants
      * leading to the readings 2005-12-31T23:59:59 and 2006-01-01T00:00:00 in the
      * {@link UTCScale UTC} time scale is 1 second, but the elapsed duration is 2
      * seconds because a leap second has been introduced at the end of 2005 in this
      * time scale.</p>
      * <p>This constructor is the reverse of the {@link #offsetFrom(AbsoluteDate,
      * TimeScale)} method.</p>
      * @param reference reference instant
      * @param apparentOffset apparent clock offset from the reference instant
      * (difference between two readings in the specified time scale)
      * @param timeScale time scale with respect to which the offset is defined
      * @see #offsetFrom(AbsoluteDate, TimeScale)
      */
     public AbsoluteDate(final AbsoluteDate reference, final double apparentOffset, final TimeScale timeScale) {
         this(reference, new TimeOffset(apparentOffset), timeScale);
     }
 
     /** Build an instance from an apparent clock offset with respect to another
      * instant <em>in the perspective of a specific {@link TimeScale time scale}</em>.
      * <p>It is important to note that the apparent clock offset <em>is</em> the
      * difference between two readings on a time scale and <em>not</em> an elapsed
      * duration. As an example, the apparent clock offset between the two instants
      * leading to the readings 2005-12-31T23:59:59 and 2006-01-01T00:00:00 in the
      * {@link UTCScale UTC} time scale is 1 second, but the elapsed duration is 2
      * seconds because a leap second has been introduced at the end of 2005 in this
      * time scale.</p>
      * <p>This constructor is the reverse of the {@link #offsetFrom(AbsoluteDate,
      * TimeScale)} method.</p>
      * @param reference reference instant
      * @param apparentOffset apparent clock offset from the reference instant
      * (difference between two readings in the specified time scale)
      * @param timeScale time scale with respect to which the offset is defined
      * @see #offsetFrom(AbsoluteDate, TimeScale)
      * @since 13.0
      */
     public AbsoluteDate(final AbsoluteDate reference, final TimeOffset apparentOffset, final TimeScale timeScale) {
         this(new DateTimeComponents(reference.getComponents(timeScale), apparentOffset),
              timeScale);
     }
 
     /** Build a date from an offset since a reference epoch.
      * @param offset offset since reference epoch 2000-01-01T12:00:00 TAI.
      * (beware, it is not {@link #J2000_EPOCH} since it is in TAI and not in TT)
      * @since 13.0
      */
     public AbsoluteDate(final TimeOffset offset) {
         super(offset.getSeconds(), offset.getAttoSeconds());
     }
 
     /** Build an instance from a CCSDS Unsegmented Time Code (CUC).
      * <p>
      * CCSDS Unsegmented Time Code is defined in the blue book:
      * CCSDS Time Code Format (CCSDS 301.0-B-4) published in November 2010
      * </p>
      * <p>
      * If the date to be parsed is formatted using version 3 of the standard
      * (CCSDS 301.0-B-3 published in 2002) or if the extension of the preamble
      * field introduced in version 4 of the standard is not used, then the
      * {@code preambleField2} parameter can be set to 0.
      * </p>
      *
      * <p>This method uses the {@link DataContext#getDefault() default data context} if
      * the CCSDS epoch is used.
      *
      * @param preambleField1 first byte of the field specifying the format, often
      * not transmitted in data interfaces, as it is constant for a given data interface
      * @param preambleField2 second byte of the field specifying the format
      * (added in revision 4 of the CCSDS standard in 2010), often not transmitted in data
      * interfaces, as it is constant for a given data interface (value ignored if presence
      * not signaled in {@code preambleField1})
      * @param timeField byte array containing the time code
      * @param agencyDefinedEpoch reference epoch, ignored if the preamble field
      * specifies the {@link #CCSDS_EPOCH CCSDS reference epoch} is used (and hence
      * may be null in this case)
      * @return an instance corresponding to the specified date
      * @see #parseCCSDSUnsegmentedTimeCode(byte, byte, byte[], AbsoluteDate, AbsoluteDate)
      */
     @DefaultDataContext
     public static AbsoluteDate parseCCSDSUnsegmentedTimeCode(final byte preambleField1,
                                                              final byte preambleField2,
                                                              final byte[] timeField,
                                                              final AbsoluteDate agencyDefinedEpoch) {
         return parseCCSDSUnsegmentedTimeCode(preambleField1, preambleField2, timeField,
                                              agencyDefinedEpoch,
                                              DataContext.getDefault().getTimeScales().getCcsdsEpoch());
     }
 
     /**
      * Build an instance from a CCSDS Unsegmented Time Code (CUC).
      * <p>
      * CCSDS Unsegmented Time Code is defined in the blue book: CCSDS Time Code Format
      * (CCSDS 301.0-B-4) published in November 2010
      * </p>
      * <p>
      * If the date to be parsed is formatted using version 3 of the standard (CCSDS
      * 301.0-B-3 published in 2002) or if the extension of the preamble field introduced
      * in version 4 of the standard is not used, then the {@code preambleField2} parameter
      * can be set to 0.
      * </p>
      *
      * @param preambleField1     first byte of the field specifying the format, often not
      *                           transmitted in data interfaces, as it is constant for a
      *                           given data interface
      * @param preambleField2     second byte of the field specifying the format (added in
      *                           revision 4 of the CCSDS standard in 2010), often not
      *                           transmitted in data interfaces, as it is constant for a
      *                           given data interface (value ignored if presence not
      *                           signaled in {@code preambleField1})
      * @param timeField          byte array containing the time code
      * @param agencyDefinedEpoch reference epoch, ignored if the preamble field specifies
      *                           the {@link DateComponents#CCSDS_EPOCH CCSDS reference epoch} is used
      *                           (and hence may be null in this case, but then {@code ccsdsEpoch} must be non-null)
      * @param ccsdsEpoch         reference epoch, ignored if the preamble field specifies
      *                           the agency epoch is used (and hence may be null in this case,
      *                           but then {@code agencyDefinedEpoch} must be non-null).
      * @return an instance corresponding to the specified date
      * @since 10.1
      */
     public static AbsoluteDate parseCCSDSUnsegmentedTimeCode(final byte preambleField1,
                                                              final byte preambleField2,
                                                              final byte[] timeField,
                                                              final AbsoluteDate agencyDefinedEpoch,
                                                              final AbsoluteDate ccsdsEpoch) {
         final CcsdsUnsegmentedTimeCode<AbsoluteDate> timeCode =
             new CcsdsUnsegmentedTimeCode<>(preambleField1, preambleField2, timeField, agencyDefinedEpoch, ccsdsEpoch);
         return timeCode.getEpoch().shiftedBy(timeCode.getTime());
 
     }
 
     /** Build an instance from a CCSDS Day Segmented Time Code (CDS).
      * <p>
      * CCSDS Day Segmented Time Code is defined in the blue book:
      * CCSDS Time Code Format (CCSDS 301.0-B-4) published in November 2010
      * </p>
      *
      * <p>This method uses the {@link DataContext#getDefault() default data context}.
      *
      * @param preambleField field specifying the format, often not transmitted in
      * data interfaces, as it is constant for a given data interface
      * @param timeField byte array containing the time code
      * @param agencyDefinedEpoch reference epoch, ignored if the preamble field
      * specifies the {@link #CCSDS_EPOCH CCSDS reference epoch} is used (and hence
      * may be null in this case)
      * @return an instance corresponding to the specified date
      * @see #parseCCSDSDaySegmentedTimeCode(byte, byte[], DateComponents, TimeScale)
      */
     @DefaultDataContext
     public static AbsoluteDate parseCCSDSDaySegmentedTimeCode(final byte preambleField, final byte[] timeField,
                                                               final DateComponents agencyDefinedEpoch) {
         return parseCCSDSDaySegmentedTimeCode(preambleField, timeField,
                                               agencyDefinedEpoch, DataContext.getDefault().getTimeScales().getUTC());
     }
 
     /** Build an instance from a CCSDS Day Segmented Time Code (CDS).
      * <p>
      * CCSDS Day Segmented Time Code is defined in the blue book:
      * CCSDS Time Code Format (CCSDS 301.0-B-4) published in November 2010
      * </p>
      * @param preambleField field specifying the format, often not transmitted in
      * data interfaces, as it is constant for a given data interface
      * @param timeField byte array containing the time code
      * @param agencyDefinedEpoch reference epoch, ignored if the preamble field
      * specifies the {@link #CCSDS_EPOCH CCSDS reference epoch} is used (and hence
      * may be null in this case)
      * @param utc      time scale used to compute date and time components.
      * @return an instance corresponding to the specified date
      * @since 10.1
      */
     public static AbsoluteDate parseCCSDSDaySegmentedTimeCode(final byte preambleField,
                                                               final byte[] timeField,
                                                               final DateComponents agencyDefinedEpoch,
                                                               final TimeScale utc) {
 
         final CcsdsSegmentedTimeCode timeCode = new CcsdsSegmentedTimeCode(preambleField, timeField,
                                                                            agencyDefinedEpoch);
         return new AbsoluteDate(timeCode.getDate(), timeCode.getTime(), utc);
     }
 
     /** Build an instance from a CCSDS Calendar Segmented Time Code (CCS).
      * <p>
      * CCSDS Calendar Segmented Time Code is defined in the blue book:
      * CCSDS Time Code Format (CCSDS 301.0-B-4) published in November 2010
      * </p>
      *
      * <p>This method uses the {@link DataContext#getDefault() default data context}.
      *
      * @param preambleField field specifying the format, often not transmitted in
      * data interfaces, as it is constant for a given data interface
      * @param timeField byte array containing the time code
      * @return an instance corresponding to the specified date
      * @see #parseCCSDSCalendarSegmentedTimeCode(byte, byte[], TimeScale)
      */
     @DefaultDataContext
     public static AbsoluteDate parseCCSDSCalendarSegmentedTimeCode(final byte preambleField, final byte[] timeField) {
         return parseCCSDSCalendarSegmentedTimeCode(preambleField, timeField,
                                                    DataContext.getDefault().getTimeScales().getUTC());
     }
 
     /** Build an instance from a CCSDS Calendar Segmented Time Code (CCS).
      * <p>
      * CCSDS Calendar Segmented Time Code is defined in the blue book:
      * CCSDS Time Code Format (CCSDS 301.0-B-4) published in November 2010
      * </p>
      * @param preambleField field specifying the format, often not transmitted in
      * data interfaces, as it is constant for a given data interface
      * @param timeField byte array containing the time code
      * @param utc      time scale used to compute date and time components.
      * @return an instance corresponding to the specified date
      * @since 10.1
      */
     public static AbsoluteDate parseCCSDSCalendarSegmentedTimeCode(final byte preambleField,
                                                                    final byte[] timeField,
                                                                    final TimeScale utc) {
         final CcsdsSegmentedTimeCode timeCode = new CcsdsSegmentedTimeCode(preambleField, timeField);
         return new AbsoluteDate(timeCode.getDate(), timeCode.getTime(), utc);
     }
 
     /** Build an instance corresponding to a Julian Day date.
      * @param jd Julian day
      * @param secondsSinceNoon seconds in the Julian day
      * (BEWARE, Julian days start at noon, so 0.0 is noon)
      * @param timeScale time scale in which the seconds in day are defined
      * @return a new instant
      */
     public static AbsoluteDate createJDDate(final int jd, final double secondsSinceNoon,
                                             final TimeScale timeScale) {
         return new AbsoluteDate(new DateComponents(DateComponents.JULIAN_EPOCH, jd),
                 TimeComponents.H12, timeScale).shiftedBy(secondsSinceNoon);
     }
 
     /** Build an instance corresponding to a Julian Day date.
      * <p>
      * This function should be preferred to {@link #createMJDDate(int, double, TimeScale)} when the target time scale
      * has a non-constant offset with respect to TAI.
      * </p>
      * <p>
      * The idea is to introduce a pivot time scale that is close to the target time scale but has a constant bias with TAI.
      * </p>
      * <p>
      * For example, to get a date from an MJD in TDB time scale, it's advised to use the TT time scale
      * as a pivot scale. TT is very close to TDB and has constant offset to TAI.
      * </p>
      * @param jd Julian day
      * @param secondsSinceNoon seconds in the Julian day
      * (BEWARE, Julian days start at noon, so 0.0 is noon)
      * @param timeScale timescale in which the seconds in day are defined
      * @param pivotTimeScale pivot timescale used as intermediate timescale
      * @return a new instant
      */
     public static AbsoluteDate createJDDate(final int jd, final double secondsSinceNoon,
                                             final TimeScale timeScale,
                                             final TimeScale pivotTimeScale) {
         // Get the date in pivot timescale
         final AbsoluteDate dateInPivotTimeScale = createJDDate(jd, secondsSinceNoon, pivotTimeScale);
 
         // Compare offsets to TAI of the two time scales
         final TimeOffset offsetFromTAI = timeScale.
                                         offsetFromTAI(dateInPivotTimeScale).
                                         subtract(pivotTimeScale.offsetFromTAI(dateInPivotTimeScale));
 
         // Return date in desired timescale
         return new AbsoluteDate(dateInPivotTimeScale, offsetFromTAI.negate());
     }
 
     /** Build an instance corresponding to a Modified Julian Day date.
      * @param mjd modified Julian day
      * @param secondsInDay seconds in the day
      * @param timeScale time scale in which the seconds in day are defined
      * @return a new instant
      * @exception OrekitIllegalArgumentException if seconds number is out of range
      */
     public static AbsoluteDate createMJDDate(final int mjd, final double secondsInDay,
                                              final TimeScale timeScale)
         throws OrekitIllegalArgumentException {
         return createMJDDate(mjd, new TimeOffset(secondsInDay), timeScale);
     }
 
     /** Build an instance corresponding to a Modified Julian Day date.
      * @param mjd modified Julian day
      * @param secondsInDay seconds in the day
      * @param timeScale time scale in which the seconds in day are defined
      * @return a new instant
      * @exception OrekitIllegalArgumentException if seconds number is out of range
      * @since 13.0
      */
     public static AbsoluteDate createMJDDate(final int mjd, final TimeOffset secondsInDay,
                                              final TimeScale timeScale)
         throws OrekitIllegalArgumentException {
         final DateComponents dc = new DateComponents(DateComponents.MODIFIED_JULIAN_EPOCH, mjd);
         final TimeComponents tc;
         if (secondsInDay.compareTo(TimeOffset.DAY) >= 0) {
             // check we are really allowed to use this number of seconds
             final TimeOffset secondsA = new TimeOffset(86399); // 23:59:59, i.e. 59s in the last minute of the day
             final TimeOffset secondsB = secondsInDay.subtract(secondsA);
             final TimeComponents safeTC = new TimeComponents(secondsA);
             final AbsoluteDate safeDate = new AbsoluteDate(dc, safeTC, timeScale);
             if (timeScale.minuteDuration(safeDate) > 59 + secondsB.toDouble()) {
                 // we are within the last minute of the day, the number of seconds is OK
                 return safeDate.shiftedBy(secondsB);
             } else {
                 // let TimeComponents trigger an OrekitIllegalArgumentException
                 // for the wrong number of seconds
                 tc = new TimeComponents(secondsA.add(secondsB));
             }
         } else {
             tc = new TimeComponents(secondsInDay);
         }
 
         // create the date
         return new AbsoluteDate(dc, tc, timeScale);
 
     }
 
     /** Build an instance corresponding to a Julian Epoch (JE).
      * <p>According to Lieske paper: <a
      * href="http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1979A%26A....73..282L&amp;defaultprint=YES&amp;filetype=.pdf.">
      * Precession Matrix Based on IAU (1976) System of Astronomical Constants</a>, Astronomy and Astrophysics,
      * vol. 73, no. 3, Mar. 1979, p. 282-284, Julian Epoch is related to Julian Ephemeris Date as:</p>
      * <pre>
      * JE = 2000.0 + (JED - 2451545.0) / 365.25
      * </pre>
      * <p>
      * This method reverts the formula above and computes an {@code AbsoluteDate} from the Julian Epoch.
      * </p>
      *
      * <p>This method uses the {@link DataContext#getDefault() default data context}.</p>
      *
      * @param julianEpoch Julian epoch, like 2000.0 for defining the classical reference J2000.0
      * @return a new instant
      * @see #J2000_EPOCH
      * @see #createBesselianEpoch(double)
      * @see TimeScales#createJulianEpoch(double)
      */
     @DefaultDataContext
     public static AbsoluteDate createJulianEpoch(final double julianEpoch) {
         return DataContext.getDefault().getTimeScales().createJulianEpoch(julianEpoch);
     }
 
     /** Build an instance corresponding to a Besselian Epoch (BE).
      * <p>According to Lieske paper: <a
      * href="http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1979A%26A....73..282L&amp;defaultprint=YES&amp;filetype=.pdf.">
      * Precession Matrix Based on IAU (1976) System of Astronomical Constants</a>, Astronomy and Astrophysics,
      * vol. 73, no. 3, Mar. 1979, p. 282-284, Besselian Epoch is related to Julian Ephemeris Date as:</p>
      * <pre>
      * BE = 1900.0 + (JED - 2415020.31352) / 365.242198781
      * </pre>
      * <p>
      * This method reverts the formula above and computes an {@code AbsoluteDate} from the Besselian Epoch.
      * </p>
      *
      * <p>This method uses the {@link DataContext#getDefault() default data context}.</p>
      *
      * @param besselianEpoch Besselian epoch, like 1950 for defining the classical reference B1950.0
      * @return a new instant
      * @see #createJulianEpoch(double)
      * @see TimeScales#createBesselianEpoch(double)
      */
     @DefaultDataContext
     public static AbsoluteDate createBesselianEpoch(final double besselianEpoch) {
         return DataContext.getDefault().getTimeScales().createBesselianEpoch(besselianEpoch);
     }
 
     /** {@inheritDoc} */
     @Override
     public AbsoluteDate shiftedBy(final double dt) {
         return new AbsoluteDate(this, dt);
     }
 
     /** {@inheritDoc} */
     @Override
     public AbsoluteDate shiftedBy(final TimeOffset dt) {
         return new AbsoluteDate(this, dt);
     }
 
     /** Get a time-shifted date.
      * <p>
      * Calling this method is equivalent to call <code>new AbsoluteDate(this, shift, timeUnit)</code>.
      * </p>
      * @param dt time shift in time units
      * @param timeUnit {@link TimeUnit} of the shift
      * @return a new date, shifted with respect to instance (which is immutable)
      * @since 12.1
      */
     public AbsoluteDate shiftedBy(final long dt, final TimeUnit timeUnit) {
         return new AbsoluteDate(this, dt, timeUnit);
     }
 
     /** Compute the physically elapsed duration between two instants.
      * <p>The returned duration is the number of seconds physically
      * elapsed between the two instants, measured in a regular time
      * scale with respect to surface of the Earth (i.e either the {@link
      * TAIScale TAI scale}, the {@link TTScale TT scale} or the {@link
      * GPSScale GPS scale}). It is the only method that gives a
      * duration with a physical meaning.</p>
      * <p>This method gives the same result (with less computation)
      * as calling {@link #offsetFrom(AbsoluteDate, TimeScale)}
      * with a second argument set to one of the regular scales cited
      * above.</p>
      * <p>This method is the reverse of the {@link #AbsoluteDate(AbsoluteDate,
      * double)} constructor.</p>
      * @param instant instant to subtract from the instance
      * @return offset in seconds between the two instants (positive
      * if the instance is posterior to the argument)
      * @see #accurateDurationFrom(AbsoluteDate)
      * @see #offsetFrom(AbsoluteDate, TimeScale)
      * @see #AbsoluteDate(AbsoluteDate, double)
      */
     public double durationFrom(final AbsoluteDate instant) {
         return accurateDurationFrom(instant).toDouble();
     }
 
     /** Compute the physically elapsed duration between two instants.
      * <p>The returned duration is the number of seconds physically
      * elapsed between the two instants, measured in a regular time
      * scale with respect to surface of the Earth (i.e either the {@link
      * TAIScale TAI scale}, the {@link TTScale TT scale} or the {@link
      * GPSScale GPS scale}). It is the only method that gives a
      * duration with a physical meaning.</p>
      * <p>This method gives the same result (with less computation)
      * as calling {@link #offsetFrom(AbsoluteDate, TimeScale)}
      * with a second argument set to one of the regular scales cited
      * above.</p>
      * <p>This method is the reverse of the {@link #AbsoluteDate(AbsoluteDate,
      * double)} constructor.</p>
      * @param instant instant to subtract from the instance
      * @return offset in seconds between the two instants (positive
      * if the instance is posterior to the argument)
      * @see #durationFrom(AbsoluteDate)
      * @see #offsetFrom(AbsoluteDate, TimeScale)
      * @see #AbsoluteDate(AbsoluteDate, double)
      * @since 13.0
      */
     public TimeOffset accurateDurationFrom(final AbsoluteDate instant) {
         return this.subtract(instant);
     }
 
     /** Compute the physically elapsed duration between two instants.
      * <p>The returned duration is the duration physically
      * elapsed between the two instants, using the given time unit and rounded to the nearest integer, measured in a regular time
      * scale with respect to surface of the Earth (i.e either the {@link
      * TAIScale TAI scale}, the {@link TTScale TT scale} or the {@link
      * GPSScale GPS scale}). It is the only method that gives a
      * duration with a physical meaning.</p>
      * <p>This method is the reverse of the {@link #AbsoluteDate(AbsoluteDate,
      * long, TimeUnit)} constructor.</p>
      * @param instant instant to subtract from the instance
      * @param timeUnit {@link TimeUnit} precision for the offset
      * @return offset in the given timeunit between the two instants (positive
      * if the instance is posterior to the argument), rounded to the nearest integer {@link TimeUnit}
      * @see #AbsoluteDate(AbsoluteDate, long, TimeUnit)
      * @since 12.1
      */
     public long durationFrom(final AbsoluteDate instant, final TimeUnit timeUnit) {
         return accurateDurationFrom(instant).getRoundedTime(timeUnit);
     }
 
     /** Compute the apparent <em>clock</em> offset between two instant <em>in the
      * perspective of a specific {@link TimeScale time scale}</em>.
      * <p>The offset is the number of seconds counted in the given
      * time scale between the locations of the two instants, with
      * all time scale irregularities removed (i.e. considering all
      * days are exactly 86400 seconds long). This method will give
      * a result that may not have a physical meaning if the time scale
      * is irregular. For example since a leap second was introduced at
      * the end of 2005, the apparent clock offset between 2005-12-31T23:59:59
      * and 2006-01-01T00:00:00 is 1 second and is the value this method
      * will return. On the other hand, the physical duration
      * of the corresponding time interval as returned by the {@link
      * #durationFrom(AbsoluteDate)} method is 2 seconds.</p>
      * <p>This method is the reverse of the {@link #AbsoluteDate(AbsoluteDate,
      * double, TimeScale)} constructor.</p>
      * @param instant instant to subtract from the instance
      * @param timeScale time scale with respect to which the offset should
      * be computed
      * @return apparent clock offset in seconds between the two instants
      * (positive if the instance is posterior to the argument)
      * @see #durationFrom(AbsoluteDate)
      * @see #accurateOffsetFrom(AbsoluteDate, TimeScale)
      * @see #AbsoluteDate(AbsoluteDate, TimeOffset, TimeScale)
      */
     public double offsetFrom(final AbsoluteDate instant, final TimeScale timeScale) {
         return accurateOffsetFrom(instant, timeScale).toDouble();
     }
 
     /** Compute the apparent <em>clock</em> offset between two instant <em>in the
      * perspective of a specific {@link TimeScale time scale}</em>.
      * <p>The offset is the number of seconds counted in the given
      * time scale between the locations of the two instants, with
      * all time scale irregularities removed (i.e. considering all
      * days are exactly 86400 seconds long). This method will give
      * a result that may not have a physical meaning if the time scale
      * is irregular. For example since a leap second was introduced at
      * the end of 2005, the apparent clock offset between 2005-12-31T23:59:59
      * and 2006-01-01T00:00:00 is 1 second and is the value this method
      * will return. On the other hand, the physical duration
      * of the corresponding time interval as returned by the {@link
      * #durationFrom(AbsoluteDate)} method is 2 seconds.</p>
      * <p>This method is the reverse of the {@link #AbsoluteDate(AbsoluteDate,
      * double, TimeScale)} constructor.</p>
      * @param instant instant to subtract from the instance
      * @param timeScale time scale with respect to which the offset should
      * be computed
      * @return apparent clock offset in seconds between the two instants
      * (positive if the instance is posterior to the argument)
      * @see #durationFrom(AbsoluteDate)
      * @see #offsetFrom(AbsoluteDate, TimeScale)
      * @see #AbsoluteDate(AbsoluteDate, TimeOffset, TimeScale)
      * @since 13.0
      */
     public TimeOffset accurateOffsetFrom(final AbsoluteDate instant, final TimeScale timeScale) {
         return new TimeOffset(this,
                               timeScale.offsetFromTAI(this),
                               instant.negate(),
                               timeScale.offsetFromTAI(instant).negate());
     }
 
     /** Compute the offset between two time scales at the current instant.
      * <p>The offset is defined as <i>l₁-l₂</i>
      * where <i>l₁</i> is the location of the instant in
      * the <code>scale1</code> time scale and <i>l₂</i> is the
      * location of the instant in the <code>scale2</code> time scale.</p>
      * @param scale1 first time scale
      * @param scale2 second time scale
      * @return offset in seconds between the two time scales at the
      * current instant
      */
     public double timeScalesOffset(final TimeScale scale1, final TimeScale scale2) {
         return scale1.offsetFromTAI(this).subtract(scale2.offsetFromTAI(this)).toDouble();
     }
 
     /** Convert the instance to a Java {@link java.util.Date Date}.
      * <p>Conversion to the Date class induces a loss of precision because
      * the Date class does not provide sub-millisecond information. Java Dates
      * are considered to be locations in some times scales.</p>
      * @param timeScale time scale to use
      * @return a {@link java.util.Date Date} instance representing the location
      * of the instant in the time scale
      */
     public Date toDate(final TimeScale timeScale) {
         final TimeOffset time = add(timeScale.offsetFromTAI(this));
         return new Date(FastMath.round((time.toDouble() + 10957.5 * Constants.JULIAN_DAY) * 1000));
     }
 
     /**
      * Convert the instance to a Java {@link java.time.Instant Instant}.
      * Nanosecond precision is preserved during this conversion
      *
      * @return a {@link java.time.Instant Instant} instance representing the location
      * of the instant in the utc time scale
      * @since 12.1
      */
     @DefaultDataContext
     public Instant toInstant() {
         return toInstant(TimeScalesFactory.getTimeScales());
     }
 
     /**
      * Convert the instance to a Java {@link java.time.Instant Instant}.
      * Nanosecond precision is preserved during this conversion
      *
      * @param timeScales the timescales to use
      * @return a {@link java.time.Instant Instant} instance representing the location
      * of the instant in the utc time scale
      * @since 12.1
      */
     public Instant toInstant(final TimeScales timeScales) {
         final UTCScale utc = timeScales.getUTC();
         final String stringWithoutUtcOffset = toStringWithoutUtcOffset(utc, 9);
 
         final LocalDateTime localDateTime = LocalDateTime.parse(stringWithoutUtcOffset, DateTimeFormatter.ISO_LOCAL_DATE_TIME);
         return localDateTime.toInstant(ZoneOffset.UTC);
     }
 
     /** Split the instance into date/time components.
      * @param timeScale time scale to use
      * @return date/time components
      */
     public DateTimeComponents getComponents(final TimeScale timeScale) {
 
         if (!isFinite()) {
             // special handling for NaN, past and future infinity
             if (isNaN()) {
                 return new DateTimeComponents(DateComponents.J2000_EPOCH, TimeComponents.NaN);
             } else if (isNegativeInfinity()) {
                 return new DateTimeComponents(DateComponents.MIN_EPOCH, TimeComponents.H00);
             } else {
                 // the fact we truncate at 59.999 seconds is for compatibility reasons
                 // with pre-13.0 Orekit versions. Indeed, this date is fake and more than
                 // 5 millions years in the future, so milliseconds are not really relevant
                 // truncating makes cleaner text output
                 return new DateTimeComponents(DateComponents.MAX_EPOCH,
                                               new TimeComponents(23, 59,
                                                                  new TimeOffset(59, TimeOffset.SECOND,
                                                                                 999, TimeOffset.MILLISECOND)));
             }
         }
 
         final TimeOffset sum = add(timeScale.offsetFromTAI(this));
 
         // split date and time
         final long offset2000A = sum.getSeconds() + 43200L;
         long time = offset2000A % 86400L;
         if (time < 0L) {
             time += 86400L;
         }
         final int date = (int) ((offset2000A - time) / 86400L);
 
         // extract calendar elements
         final DateComponents dateComponents = new DateComponents(DateComponents.J2000_EPOCH, date);
 
         // extract time element, accounting for leap seconds
         final TimeOffset leap = timeScale.insideLeap(this) ? timeScale.getLeap(this) : TimeOffset.ZERO;
         final int minuteDuration = timeScale.minuteDuration(this);
         final TimeComponents timeComponents = new TimeComponents(new TimeOffset(time, sum.getAttoSeconds()),
                                                                  leap, minuteDuration);
 
         // build the components
         return new DateTimeComponents(dateComponents, timeComponents);
 
     }
 
     /** Split the instance into date/time components for a local time.
      *
      * <p>This method uses the {@link DataContext#getDefault() default data context}.
      *
      * @param minutesFromUTC offset in <em>minutes</em> from UTC (positive Eastwards UTC,
      * negative Westward UTC)
      * @return date/time components
      * @since 7.2
      * @see #getComponents(int, TimeScale)
      */
     @DefaultDataContext
     public DateTimeComponents getComponents(final int minutesFromUTC) {
         return getComponents(minutesFromUTC,
                 DataContext.getDefault().getTimeScales().getUTC());
     }
 
     /**
      * Split the instance into date/time components for a local time.
      *
      * @param minutesFromUTC offset in <em>minutes</em> from UTC (positive Eastwards UTC,
      *                       negative Westward UTC)
      * @param utc            time scale used to compute date and time components.
      * @return date/time components
      * @since 10.1
      */
     public DateTimeComponents getComponents(final int minutesFromUTC,
                                             final TimeScale utc) {
 
         final DateTimeComponents utcComponents = getComponents(utc);
 
         // shift the date according to UTC offset, but WITHOUT touching the seconds,
         // as they may exceed 60.0 during a leap seconds introduction,
         // and we want to preserve these special cases
         final TimeOffset seconds = utcComponents.getTime().getSplitSecond();
 
         int minute = utcComponents.getTime().getMinute() + minutesFromUTC;
         final int hourShift;
         if (minute < 0) {
             hourShift = (minute - 59) / 60;
         } else if (minute > 59) {
             hourShift = minute / 60;
         } else {
             hourShift = 0;
         }
         minute -= 60 * hourShift;
 
         int hour = utcComponents.getTime().getHour() + hourShift;
         final int dayShift;
         if (hour < 0) {
             dayShift = (hour - 23) / 24;
         } else if (hour > 23) {
             dayShift = hour / 24;
         } else {
             dayShift = 0;
         }
         hour -= 24 * dayShift;
 
         return new DateTimeComponents(new DateComponents(utcComponents.getDate(), dayShift),
                                       new TimeComponents(hour, minute, seconds, minutesFromUTC));
 
     }
 
     /** Split the instance into date/time components for a time zone.
      *
      * <p>This method uses the {@link DataContext#getDefault() default data context}.
      *
      * @param timeZone time zone
      * @return date/time components
      * @since 7.2
      * @see #getComponents(TimeZone, TimeScale)
      */
     @DefaultDataContext
     public DateTimeComponents getComponents(final TimeZone timeZone) {
         return getComponents(timeZone, DataContext.getDefault().getTimeScales().getUTC());
     }
 
     /**
      * Split the instance into date/time components for a time zone.
      *
      * @param timeZone time zone
      * @param utc      time scale used to computed date and time components.
      * @return date/time components
      * @since 10.1
      */
     public DateTimeComponents getComponents(final TimeZone timeZone,
                                             final TimeScale utc) {
         final AbsoluteDate javaEpoch = new AbsoluteDate(DateComponents.JAVA_EPOCH, utc);
         final long milliseconds = FastMath.round(1000 * offsetFrom(javaEpoch, utc));
         return getComponents(timeZone.getOffset(milliseconds) / 60000, utc);
     }
 
     /** {@inheritDoc} */
     public AbsoluteDate getDate() {
         return this;
     }
 
     /** Check if the instance represents the same time as another.
      * @param other the instant to compare this date to
      * @return true if the instance and the argument refer to the same instant
      * @see #isCloseTo(TimeStamped, double)
      * @since 10.1
      */
     public boolean isEqualTo(final TimeStamped other) {
         return this.equals(other.getDate());
     }
 
     /** Check if the instance time is close to another.
      * @param other the instant to compare this date to
      * @param tolerance the separation, in seconds, under which the two instants will be considered close to each other
      * @return true if the duration between the instance and the argument is strictly below the tolerance
      * @see #isEqualTo(TimeStamped)
      * @since 10.1
      */
     public boolean isCloseTo(final TimeStamped other, final double tolerance) {
         return FastMath.abs(this.durationFrom(other.getDate())) < tolerance;
     }
 
     /** Check if the instance represents a time that is strictly before another.
      * @param other the instant to compare this date to
      * @return true if the instance is strictly before the argument when ordering chronologically
      * @see #isBeforeOrEqualTo(TimeStamped)
      * @since 10.1
      */
     public boolean isBefore(final TimeStamped other) {
         return this.compareTo(other.getDate()) < 0;
     }
 
     /** Check if the instance represents a time that is strictly after another.
      * @param other the instant to compare this date to
      * @return true if the instance is strictly after the argument when ordering chronologically
      * @see #isAfterOrEqualTo(TimeStamped)
      * @since 10.1
      */
     public boolean isAfter(final TimeStamped other) {
         return this.compareTo(other.getDate()) > 0;
     }
 
     /** Check if the instance represents a time that is before or equal to another.
      * @param other the instant to compare this date to
      * @return true if the instance is before (or equal to) the argument when ordering chronologically
      * @see #isBefore(TimeStamped)
      * @since 10.1
      */
     public boolean isBeforeOrEqualTo(final TimeStamped other) {
         return this.isEqualTo(other) || this.isBefore(other);
     }
 
     /** Check if the instance represents a time that is after or equal to another.
      * @param other the instant to compare this date to
      * @return true if the instance is after (or equal to) the argument when ordering chronologically
      * @see #isAfterOrEqualTo(TimeStamped)
      * @since 10.1
      */
     public boolean isAfterOrEqualTo(final TimeStamped other) {
         return this.isEqualTo(other) || this.isAfter(other);
     }
 
     /** Check if the instance represents a time that is strictly between two others representing
      * the boundaries of a time span. The two boundaries can be provided in any order: in other words,
      * whether <code>boundary</code> represents a time that is before or after <code>otherBoundary</code> will
      * not change the result of this method.
      * @param boundary one end of the time span
      * @param otherBoundary the other end of the time span
      * @return true if the instance is strictly between the two arguments when ordering chronologically
      * @see #isBetweenOrEqualTo(TimeStamped, TimeStamped)
      * @since 10.1
      */
     public boolean isBetween(final TimeStamped boundary, final TimeStamped otherBoundary) {
         final TimeStamped beginning;
         final TimeStamped end;
         if (boundary.getDate().isBefore(otherBoundary)) {
             beginning = boundary;
             end = otherBoundary;
         } else {
             beginning = otherBoundary;
             end = boundary;
         }
         return this.isAfter(beginning) && this.isBefore(end);
     }
 
     /** Check if the instance represents a time that is between two others representing
      * the boundaries of a time span, or equal to one of them. The two boundaries can be provided in any order:
      * in other words, whether <code>boundary</code> represents a time that is before or after
      * <code>otherBoundary</code> will not change the result of this method.
      * @param boundary one end of the time span
      * @param otherBoundary the other end of the time span
      * @return true if the instance is between the two arguments (or equal to at least one of them)
      * when ordering chronologically
      * @see #isBetween(TimeStamped, TimeStamped)
      * @since 10.1
      */
     public boolean isBetweenOrEqualTo(final TimeStamped boundary, final TimeStamped otherBoundary) {
         return this.isEqualTo(boundary) || this.isEqualTo(otherBoundary) || this.isBetween(boundary, otherBoundary);
     }
 
     /**
      * Get a String representation of the instant location with up to 18 digits of
      * precision for the seconds value.
      *
      * <p> Since this method is used in exception messages and error handling every
      * effort is made to return some representation of the instant. If UTC is available
      * from the default data context then it is used to format the string in UTC. If not
      * then TAI is used. Finally if the prior attempts fail this method falls back to
      * converting this class's internal representation to a string.
      *
      * <p>This method uses the {@link DataContext#getDefault() default data context}.
      *
      * @return a string representation of the instance, in ISO-8601 format if UTC is
      * available from the default data context.
      * @see #toString(TimeScale)
      * @see #toStringRfc3339(TimeScale)
      * @see DateTimeComponents#toString(int, int)
      */
     @DefaultDataContext
     public String toString() {
         // CHECKSTYLE: stop IllegalCatch check
         try {
             // try to use UTC first at that is likely most familiar to the user.
             return toString(DataContext.getDefault().getTimeScales().getUTC()) + "Z";
         } catch (RuntimeException e1) {
             // catch OrekitException, OrekitIllegalStateException, etc.
             try {
                 // UTC failed, try to use TAI
                 return toString(new TAIScale()) + " TAI";
             } catch (RuntimeException e2) {
                 // catch OrekitException, OrekitIllegalStateException, etc.
                 // Likely failed to convert to ymdhms.
                 // Give user some indication of what time it is.
                 return "(" + this.getSeconds() + "s + " + this.getAttoSeconds() + "as) seconds past epoch";
             }
         }
         // CHECKSTYLE: resume IllegalCatch check
     }
 
     /**
      * Get a String representation of the instant location in ISO-8601 format without the
      * UTC offset and with up to 16 digits of precision for the seconds value.
      *
      * @param timeScale time scale to use
      * @return a string representation of the instance.
      * @see #toStringRfc3339(TimeScale)
      * @see DateTimeComponents#toString(int, int)
      */
     public String toString(final TimeScale timeScale) {
         return getComponents(timeScale).toStringWithoutUtcOffset();
     }
 
     /** Get a String representation of the instant location for a local time.
      *
      * <p>This method uses the {@link DataContext#getDefault() default data context}.
      *
      * @param minutesFromUTC offset in <em>minutes</em> from UTC (positive Eastwards UTC,
      * negative Westward UTC).
      * @return string representation of the instance,
      * in ISO-8601 format with milliseconds accuracy
      * @since 7.2
      * @see #toString(int, TimeScale)
      */
     @DefaultDataContext
     public String toString(final int minutesFromUTC) {
         return toString(minutesFromUTC,
                 DataContext.getDefault().getTimeScales().getUTC());
     }
 
     /**
      * Get a String representation of the instant location for a local time.
      *
      * @param minutesFromUTC offset in <em>minutes</em> from UTC (positive Eastwards UTC,
      *                       negative Westward UTC).
      * @param utc            time scale used to compute date and time components.
      * @return string representation of the instance, in ISO-8601 format with milliseconds
      * accuracy
      * @since 10.1
      * @see #getComponents(int, TimeScale)
      * @see DateTimeComponents#toString(int, int)
      */
     public String toString(final int minutesFromUTC, final TimeScale utc) {
         final int minuteDuration = utc.minuteDuration(this);
         return getComponents(minutesFromUTC, utc).toString(minuteDuration);
     }
 
     /** Get a String representation of the instant location for a time zone.
      *
      * <p>This method uses the {@link DataContext#getDefault() default data context}.
      *
      * @param timeZone time zone
      * @return string representation of the instance,
      * in ISO-8601 format with milliseconds accuracy
      * @since 7.2
      * @see #toString(TimeZone, TimeScale)
      */
     @DefaultDataContext
     public String toString(final TimeZone timeZone) {
         return toString(timeZone, DataContext.getDefault().getTimeScales().getUTC());
     }
 
     /**
      * Get a String representation of the instant location for a time zone.
      *
      * @param timeZone time zone
      * @param utc      time scale used to compute date and time components.
      * @return string representation of the instance, in ISO-8601 format with milliseconds
      * accuracy
      * @since 10.1
      * @see #getComponents(TimeZone, TimeScale)
      * @see DateTimeComponents#toString(int, int)
      */
     public String toString(final TimeZone timeZone, final TimeScale utc) {
         final int minuteDuration = utc.minuteDuration(this);
         return getComponents(timeZone, utc).toString(minuteDuration);
     }
 
     /**
      * Represent the given date as a string according to the format in RFC 3339. RFC3339
      * is a restricted subset of ISO 8601 with a well defined grammar. Enough digits are
      * included in the seconds value to avoid rounding up to the next minute.
      *
      * <p>This method is different than {@link AbsoluteDate#toString(TimeScale)} in that
      * it includes a {@code "Z"} at the end to indicate the time zone and enough precision
      * to represent the point in time without rounding up to the next minute.
      *
      * <p>RFC3339 is unable to represent BC years, years of 10000 or more, time zone
      * offsets of 100 hours or more, or NaN. In these cases the value returned from this
      * method will not be valid RFC3339 format.
      *
      * @param utc time scale.
      * @return RFC 3339 format string.
      * @see <a href="https://tools.ietf.org/html/rfc3339#page-8">RFC 3339</a>
      * @see DateTimeComponents#toStringRfc3339()
      * @see #toString(TimeScale)
      * @see #getComponents(TimeScale)
      */
     public String toStringRfc3339(final TimeScale utc) {
         return this.getComponents(utc).toStringRfc3339();
     }
 
     /**
      * Return a string representation of this date-time, rounded to the given precision.
      *
      * <p>The format used is ISO8601 without the UTC offset.</p>
      *
      * <p>Calling {@code toStringWithoutUtcOffset(DataContext.getDefault().getTimeScales().getUTC(),
      * 3)} will emulate the behavior of {@link #toString()} in Orekit 10 and earlier. Note
      * this method is more accurate as it correctly handles rounding during leap seconds.
      *
      * @param timeScale      to use to compute components.
      * @param fractionDigits the number of digits to include after the decimal point in
      *                       the string representation of the seconds. The date and time
      *                       is first rounded as necessary. {@code fractionDigits} must be
      *                       greater than or equal to {@code 0}.
      * @return string representation of this date, time, and UTC offset
      * @see #toString(TimeScale)
      * @see #toStringRfc3339(TimeScale)
      * @see DateTimeComponents#toString(int, int)
      * @see DateTimeComponents#toStringWithoutUtcOffset(int, int)
      * @since 11.1
      */
     public String toStringWithoutUtcOffset(final TimeScale timeScale,
                                            final int fractionDigits) {
         return this.getComponents(timeScale)
                 .toStringWithoutUtcOffset(timeScale.minuteDuration(this), fractionDigits);
     }
 
     /**
      * Return the given date as a Modified Julian Date <b>expressed in UTC</b>.
      *
      * @return double representation of the given date as Modified Julian Date.
      *
      * @since 12.2
      */
     @DefaultDataContext
     public double getMJD() {
         return this.getJD() - DateComponents.JD_TO_MJD;
     }
 
     /**
      * Return the given date as a Modified Julian Date expressed in given timescale.
      *
      * @param ts time scale
      *
      * @return double representation of the given date as Modified Julian Date.
      *
      * @since 12.2
      */
     public double getMJD(final TimeScale ts) {
         return this.getJD(ts) - DateComponents.JD_TO_MJD;
     }
 
     /**
      * Return the given date as a Julian Date <b>expressed in UTC</b>.
      *
      * @return double representation of the given date as Julian Date.
      *
      * @since 12.2
      */
     @DefaultDataContext
     public double getJD() {
         return getJD(TimeScalesFactory.getUTC());
     }
 
     /**
      * Return the given date as a Julian Date expressed in given timescale.
      *
      * @param ts time scale
      *
      * @return double representation of the given date as Julian Date.
      *
      * @since 12.2
      */
     public double getJD(final TimeScale ts) {
         return this.getComponents(ts).offsetFrom(DateTimeComponents.JULIAN_EPOCH) / Constants.JULIAN_DAY;
     }
 
     /** Get day of year, preserving continuity as much as possible.
      * <p>
      * This is a continuous extension of the integer value returned by
      * {@link #getComponents(TimeZone) getComponents(utc)}{@link DateTimeComponents#getDate() .getDate()}{@link DateComponents#getDayOfYear() .getDayOfYear()}.
      * In order to have it remain as close as possible to its integer counterpart,
      * day 1.0 is considered to occur on January 1st at noon.
      * </p>
      * <p>
      * Continuity is preserved from day to day within a year, but of course
      * there is a discontinuity at year change, where it switches from 365.49999…
      * (or 366.49999… on leap years) to 0.5
      * </p>
      * @param utc time scale to compute date components
      * @return day of year, with day 1.0 occurring on January first at noon
      * @since 13.0
      */
     public double getDayOfYear(final TimeScale utc) {
         final int          year        = getComponents(utc).getDate().getYear();
         final AbsoluteDate newYearsEve = new AbsoluteDate(year - 1, 12, 31, 12, 0, 0.0, utc);
         return durationFrom(newYearsEve) / Constants.JULIAN_DAY;
     }
 
 }